Estimates of effective radiative forcing by aerosol-cloud interactions (ERFaci) have varied widely. Here an AeroCOM intercomparison project is organized to compare ERFaci estimates in several global climate models with a focus on aerosol effects on liquid clouds. Based on multi-model analysis, we find that one of the largest uncertainties in the estimate of ERFaci comes from the uncertainty in the response of cloud liquid water path to anthropogenic aerosols. This response is found to have strong regime dependence with even larger uncertainty under different dynamical regimes. Several different metrics in the literature (e.g., rain frequency susceptibility to aerosols, Spop) are intercompared and used to constrain this response.